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https://qiita.com/Kiri8128/items/1738d5403764a0e26b4c\nP = mod = 998244353\np, g, ig = 998244353, 3, 332748118\nW = [pow(g, (p - 1) >> i, p) for i in range(24)]\niW = [pow(ig, (p - 1) >> i, p) for i in range(24)]\n \ndef convolve(a, b):\n def fft(f):\n for l in range(k, 0, -1):\n d = 1 << l - 1\n U = [1]\n for i in range(d):\n U.append(U[-1] * W[l] % p)\n \n for i in range(1 << k - l):\n for j in range(d):\n s = i * 2 * d + j\n t = s + d\n f[s], f[t] = (f[s] + f[t]) % p, U[j] * (f[s] - f[t]) % p\n \n def ifft(f):\n for l in range(1, k + 1):\n d = 1 << l - 1\n U = [1]\n for i in range(d):\n U.append(U[-1] * iW[l] % p)\n \n for i in range(1 << k - l):\n for j in range(d):\n s = i * 2 * d + j\n t = s + d\n f[s], f[t] = (f[s] + f[t] * U[j]) % p, (f[s] - f[t] * U[j]) % p\n \n n0 = len(a) + len(b) - 1\n if len(a) < 50 or len(b) < 50:\n ret = [0] * n0\n if len(a) > len(b): a, b = b, a\n for i, aa in enumerate(a):\n for j, bb in enumerate(b):\n ret[i+j] = (ret[i+j] + aa * bb) % p\n return ret\n \n k = (n0).bit_length()\n n = 1 << k\n a = a + [0] * (n - len(a))\n b = b + [0] * (n - len(b))\n fft(a), fft(b)\n for i in range(n):\n a[i] = a[i] * b[i] % p\n ifft(a)\n invn = pow(n, p - 2, p)\n for i in range(n0):\n a[i] = a[i] * invn % p\n del a[n0:]\n return a\n \nclass RelaxedMultiplication():\n # h = f * g\n def __init__(self):\n self.f = []\n self.g = []\n self.h = []\n self.n = 0\n \n def calc(self, l1, r1, l2, r2):\n self.h += [0] * (r1 + r2 - 1 - len(self.h))\n for i, a in enumerate(convolve(self.f[l1:r1], self.g[l2:r2]), l1 + l2):\n self.h[i] = (self.h[i] + a) % p\n \n def append(self, a, b):\n self.f.append(a)\n self.g.append(b)\n self.n += 1\n n = self.n\n m = (n + 1) & -(n + 1)\n s = 0\n if m <= n:\n a = 1\n while a <= m:\n self.calc(n - a, n, s, s + a)\n self.calc(s, s + a, n - a, n)\n s += a\n a <<= 1\n else:\n a = 1\n while a < m >> 1:\n self.calc(n - a, n, s, s + a)\n self.calc(s, s + a, n - a, n)\n s += a\n a <<= 1\n self.calc(n - a, n, s, s + a)\n return self.h[n-1]\n\nn = int(input())\n\nR = RelaxedMultiplication()\n\nf = [0, 1]\n\ng = [0] * (n + 1)\n\nfor i in range(1, n + 1):\n for k in range(1, n + 1):\n if i * k > n:\n break\n g[i * k] += f[i] * i\n g[i * k] %= mod\n \n h = R.append(f[i], g[i])\n f.append(h * pow(i, -1, mod) % mod)\n \nff = convolve(f, f)[:n + 1]\nf2 = [0] * (n + 1)\n\nfor i in range(n):\n if i * 2 <= n:\n f2[i * 2] = f[i]\n\nans = [0] * (n + 1)\ni2 = pow(2, -1, mod)\nans[0] = 1\nfor i in range(1, n + 1):\n ans[i] = f[i] - (ff[i] - f2[i]) * i2\n ans[i] %= mod\n \nprint(*ans)","codes",[],"stdin","20","compiler","cpython-3.10.2","createdAt",1703420098,"title","description","shirotsume4","isPrivate","compilerInfo",{"_11":3391,"_13":3400,"_15":1315,"_17":1330,"_19":3401,"_22":25,"_24":23,"_26":3402,"_28":3403},"3.10.2",[1318],"python3 prog.py",[],"results",[3406,3410,3413,3416],{"_31":3407,"_3408":3409},"Control","data","Start",{"_31":3411,"_3408":3412},"StdOut","1 1 1 1 2 3 6 11 23 47 106 235 551 1301 3159 7741 19320 48629 123867 317955 823065\n",{"_31":3414,"_3408":3415},"ExitCode","0",{"_31":3407,"_3408":3417},"Finish","hpplib",[3420,3435,3446,3455,3464,3473,3482,3491,3501,3510,3521,3532,3543,3554,3563,3574],{"_11":3421,"_3422":3423,"_3395":3424,"_3425":3426,"_3427":3428,"_3433":3434},"CLI11","repository","CLIUtils/CLI11","CLI11 is a command line parser for C++11 and beyond that provides a rich feature set with a simple and intuitive interface.","headerDescription","","wandbox",{"_3429":3430,"_3431":3432},"tagName","v2.5.0","publishedAt","2025-02-27T12:29:12Z","clangd",{"_3429":3430,"_3431":3432},{"_11":3436,"_3422":3437,"_3395":3438,"_3425":3439,"_3427":3440,"_3433":3443},"cxxopts","jarro2783/cxxopts","Lightweight C++ command line option parser","",{"_3429":3441,"_3431":3442},"v3.3.1","2025-05-26T08:12:04Z",{"_3429":3444,"_3431":3445},"v3.2.0","2024-02-15T05:32:43Z",{"_11":3447,"_3422":3448,"_3395":3449,"_3425":3450,"_3427":3451,"_3433":3454},"nanobench","martinus/nanobench","Simple, fast, accurate single-header microbenchmarking functionality for C++11/14/17/20","",{"_3429":3452,"_3431":3453},"v4.3.11","2023-02-16T19:06:26Z",{"_3429":3452,"_3431":3453},{"_11":3456,"_3422":3457,"_3395":3458,"_3425":3459,"_3427":3460,"_3433":3463},"toml11","ToruNiina/toml11","TOML for Modern C++","",{"_3429":3461,"_3431":3462},"v4.4.0","2025-02-15T16:20:52Z",{"_3429":3461,"_3431":3462},{"_11":3465,"_3422":3466,"_3395":3467,"_3425":3468,"_3427":3469,"_3433":3472},"toml++","marzer/tomlplusplus","Header-only TOML config file parser and serializer for C++17.","",{"_3429":3470,"_3431":3471},"v3.4.0","2023-10-13T13:45:17Z",{"_3429":3470,"_3431":3471},{"_11":3474,"_3422":3475,"_3395":3476,"_3425":3477,"_3427":3478,"_3433":3481},"rapidjson","Tencent/rapidjson","A fast JSON parser/generator for C++ with both SAX/DOM style API","",{"_3429":3479,"_3431":3480},"v1.1.0","2016-08-25T08:01:22Z",{"_3429":3479,"_3431":3480},{"_11":3483,"_3422":3484,"_3395":3485,"_3425":3486,"_3427":3487,"_3433":3490},"picojson","kazuho/picojson","a header-file-only, JSON parser serializer in C++","",{"_3429":3488,"_3431":3489},"v1.3.0","2015-02-25T04:12:53Z",{"_3429":3488,"_3431":3489},{"_11":3492,"_3422":3492,"_3395":3493,"_3425":3494,"_3427":3495,"_3433":3498},"nlohmann/json","JSON for Modern C++","",{"_3429":3496,"_3431":3497},"v3.12.0","2025-04-11T08:43:39Z",{"_3429":3499,"_3431":3500},"v3.11.3","2023-11-28T21:38:09Z",{"_11":3502,"_3422":3503,"_3395":3504,"_3425":3505,"_3427":3506,"_3433":3509},"csv-parser","vincentlaucsb/csv-parser","A high-performance, fully-featured CSV parser and serializer for modern C++.","",{"_3429":3507,"_3431":3508},"2.3.0","2024-06-15T20:23:18Z",{"_3429":3507,"_3431":3508},{"_11":3511,"_3422":3512,"_3395":3513,"_3425":3514,"_3427":3515,"_3433":3518},"rapidcsv","d99kris/rapidcsv","C++ CSV parser library","",{"_3429":3516,"_3431":3517},"v8.87","2025-05-17T05:37:53Z",{"_3429":3519,"_3431":3520},"v8.84","2024-09-28T05:31:16Z",{"_11":3522,"_3422":3523,"_3395":3524,"_3425":3525,"_3427":3526,"_3433":3529},"fmt","fmtlib/fmt","A modern formatting library","",{"_3429":3527,"_3431":3528},"11.2.0","2025-05-03T16:40:00Z",{"_3429":3530,"_3431":3531},"11.1.4","2025-02-26T18:33:33Z",{"_11":3533,"_3422":3534,"_3395":3535,"_3425":3536,"_3427":3537,"_3433":3540},"NumCpp","dpilger26/NumCpp","C++ implementation of the Python Numpy library","",{"_3429":3538,"_3431":3539},"Version_2.14.1","2025-05-05T03:42:56Z",{"_3429":3541,"_3431":3542},"Version_2.14.0","2025-02-09T04:16:30Z",{"_11":3544,"_3422":3545,"_3395":3546,"_3425":3547,"_3427":3548,"_3433":3551},"spdlog","gabime/spdlog","Fast C++ logging library.","",{"_3429":3549,"_3431":3550},"v1.15.3","2025-05-09T08:59:29Z",{"_3429":3552,"_3431":3553},"v1.15.1","2025-02-01T12:08:58Z",{"_11":3555,"_3422":3556,"_3395":3557,"_3425":3558,"_3427":3559,"_3433":3562},"expected-lite","martinmoene/expected-lite","expected lite - Expected objects in C++11 and later in a single-file header-only library","",{"_3429":3560,"_3431":3561},"v0.8.0","2024-06-05T21:24:45Z",{"_3429":3560,"_3431":3561},{"_11":3564,"_3422":3565,"_3395":3566,"_3425":3567,"_3427":3568,"_3433":3571},"gsl-lite","gsl-lite/gsl-lite","ISO C++ Core Guidelines Library implementation for C++98, C++11 up","",{"_3429":3569,"_3431":3570},"v1.0.1","2025-05-19T21:18:08Z",{"_3429":3572,"_3431":3573},"v0.42.0","2024-11-01T20:24:11Z",{"_11":3575,"_3422":3576,"_3395":3577,"_3425":3578,"_3427":3579,"_3433":3582},"ut","boost-ext/ut","C++20 μ(micro)/Unit Testing framework","",{"_3429":3580,"_3431":3581},"v2.3.1","2025-04-02T13:02:52Z",{"_3429":3583,"_3431":3584},"v2.3.0","2025-02-04T11:58:39Z","env",{"_3587":3588,"_3589":3590,"_3591":3592,"_3593":3594,"_3595":3596,"_3597":3598,"_3599":3600,"_3601":3602,"_3603":3604},"KV_CACHE",{},"KV_SESSION",{},"R2_BUCKET",{},"WANDBOX_GITHUB_CLIENT_ID","f9d429d939d997e6b08e","WANDBOX_GITHUB_CLIENT_SECRET","d99b3d12225671cde514d9e2b3d5cc8356f4ed5f","WANDBOX_KV_COOKIE_SECRET","FaCnykHoYzqiXReGkgvmcYGvQdQ4yZUE","WANDBOX_R2_PREFIX","master/","WANDBOX_URL_PREFIX","https://api.wandbox.org","ASSETS",{},"root","actionData","errors"]